Answer:
[tex]y>\frac{2}{3}x+3[/tex]
Step-by-step explanation:
step 1
Determine the slope of the dashed line
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-3,1) and (0,3)
substitute
[tex]m=\frac{3-1}{0+3}[/tex]
[tex]m=\frac{2}{3}[/tex]
step 2
Find the equation of the dashed line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]b=3[/tex] ---> given problem
substitute
[tex]y=\frac{2}{3}x+3[/tex]
step 3
Find the equation of the inequality
we know that
Is a dashed line and everything to the left of the line is shaded
so
[tex]y>\frac{2}{3}x+3[/tex]
see the attached figure to better understand the problem
